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Topic 7 Homework (Nonadaptive)

Question 8 of 16 (1 point)**|**Question Attempt: 1 of Unlimited

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Question 8

For the 

50

 U.S. states, the least-squares regression equation relating the 1980 per capita income and the 1999 per capita income is 

=y+7.971.97x

, with 

x

 denoting 1980 per capita income and 

y

 denoting 1999 per capita income. The standard error of the slope of this least-squares regression line is approximately 

1.64

. (Source: U.S. Bureau of Economic Analysis, Survey of Current Business, May 2000.) 

Based on this information, test for a significant linear relationship between the variables 

x

 and 

y

 by doing a hypothesis test regarding the population slope 

β1

. (Assume that the variable 

y

 follows a normal distribution for each value of 

x

 and that the other regression assumptions are satisfied.) Use the 

0.10

 level of significance, and perform a two-tailed test. Then complete the parts below. 

(If necessary, consult a list of formulas.)

(a)

State the null hypothesis 

H0

 and the alternative hypothesis 

H1

.

H0:β1=0

H1:β1≠0

(b)

Determine the type of test statistic to use.

▼t

Degrees of freedom: 

(c)

Find the value of the test statistic. (Round to three or more decimal places.)

1.201

(d)

Find the two critical values at the 

0.10

 level of significance. (Round to three or more decimal places.)

and

(e)

Based on the data, can we conclude (using the 

0.10

 level) that there is a significant linear relationship between 1980 per capita income and 1999 per capita income for U.S. states?

Yes  No

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